Yes, the brand is the icon that appears in the devices catalog of the app, a user can find your connector by brand and by category. By default, Schema integrations are found in the category “others”.
A brand can have more than one Schema connector, so, this helps you identify the one the user needs to install to get his devices.
Once your device integration is published, when you enter the brand, you’ll see the connector.
Here there’s an example of the brand Exosite ExoHome. In this case, the connector has the same name as the brand:
If they belong to the same connector, yes, it needs to have the same name. This field is also included in the certification application form, so, make sure you fill up that box with the same name.
Not sure, I would need to check this one with the engineering team.
About this one, there’s an option to see the device models supported as shown in the sample below but I’ll ask the team where are those values coming from: